Question: Multiply the following complex numbers: $({-1-2i}) \cdot ({2-5i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-1-2i}) \cdot ({2-5i}) = $ $ ({-1} \cdot {2}) + ({-1} \cdot {-5}i) + ({-2}i \cdot {2}) + ({-2}i \cdot {-5}i) $ Then simplify the terms: $ (-2) + (5i) + (-4i) + (10 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -2 + (5 - 4)i + 10i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -2 + (5 - 4)i - 10 $ The result is simplified: $ (-2 - 10) + (1i) = -12+i $